Charter arguments can be raised even if non-charter arguments would not succeed

38 Conduct of public authorities
(1) Subject to this section, it is unlawful for a public authority to act in a way that is incompatible with a human right or, in making a decision, to fail to give proper consideration to a relevant human right.
(2) Subsection (1) does not apply if, as a result of a statutory provision or a provision made by or under an Act of the Commonwealth or otherwise under law, the public authority could not reasonably have acted differently or made a different decision.Example
Where the public authority is acting to give effect to a statutory provision that is incompatible with a human right.

39 Legal proceedings
(1) If, otherwise than because of this Charter, a person may seek any relief or remedy in respect of an act or decision of a public authority on the ground that the act or decision was unlawful, that person may seek that relief or remedy on a ground of unlawfulness arising because of this Charter.
(2) This section does not affect any right that a person has, otherwise than because of this Charter, to seek any relief or remedy in respect of an act or decision of a public authority, including a right—
(a) to seek judicial review under the Administrative Law Act 1978 or under Order 56 of Chapter I of the Rules of the Supreme Court; and
(b) to seek a declaration of unlawfulness and associated relief including an injunction, a stay of proceedings or exclusion of evidence.

It is now well-established that all that is required to raise a charter ground in an otherwise non-charter proceeding is the mere availability, in the abstract sense, of relief or remedy in the otherwise non-charter proceeding. Thus for example, if a decision is subject to judicial review whether by rule 56 of the Supreme Court (General Civil Procedure) Rules 2015 or the Administrative Law Act 1978–as most decisions are–then even if a common law ground that would give rise to jurisdictional error cannot be made out, the decision may be unlawful by reason of a Charter ground and nothing else.

the mere exercise of an available right to seek relief or remedy in respect of an act or decision of a public authority on a ground that is independent of the Charter is sufficient to satisfy the condition in s 39 of the Charter; that is, s 39 does not depend upon a successful exercise of that right based on the non-Charter ground.